A consonant is a speech sound that is not a vowel. It also refers to letters of the alphabet that represent those sounds: Z, B, T, G, and H are all consonants.
Consonants are all the non-vowel sounds, or their corresponding letters: A, E, I, O, U and sometimes Y are not consonants. In hat, H and T are consonants. Consonant can also be an adjective that describes things that seem like they should go together, things that are "agreeable." You could say a nation's offer of aid is consonant with their treaties. When you hear consonant sounds in music, they are pleasing, the opposite of "dissonant" sounds which are harsh.